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Nuclear Physics III

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~ 1ms
Lifetime of neutron
Leak from reactor, absorbed, cause further fissions.
Neutron fates
~20,000 km s^-1
Initial speed of neutron
~2 km s^-1
Speed of moderated neutron
ΦΣ_a
Absorption rate
vΦΣ_f
Production rate
dn/dt
Rate of increase in neutron number density
∇⋅J
Rate of flow of neutrons away from the location
dn/dt = vΦΣ_f - ΦΣ_a - ∇⋅J
Balance equation
Neutrons tend to perform a net drift from regions of high flux to regions of low flux at a rate proportional to the flux gradient.
Assumption of diffusion approximation
J = -D∇Φ
Diffusion approximation (equation)
dn/dt = vΦΣ_f - ΦΣ_a + D∇^2Φ
The Diffusion Equation
size of reactor (the larger, the less significant is leakage relative to other neutron fates); amount of parasitic absorption (in structure and coolant);
amount of fuel (to cause further fissions)
Criticality depends on...
Maximum at centre, zero at edges; a cosine axially (zero at the ends, maximum in the middle); a Bessel function radially (zero at the outer radius, maximum in the middle)
Flux distribution when critical in cylindrical reactor
Cosine
Linear heat flux variation in axial coolant channels
Ability to remove the heat generated without exceeding safe coolant or structure temperatures
Limiting factor of absolute reactor power